Page 88 - Fundamentals of Geomorphology

GEOMORPHIC MATERIALS AND PROCESSES 71

( ) Hydraulic jump which was devised by the American hydraulic engineer
a
Robert Manning at the end of the nineteenth century,
Supercritical flow Subcritical flow
is a more commonly used formula for estimating flow
velocity:
R 2/3 1/2
s
Stream bed
Stream bed
v =
n
( ) Hydraulic drop where R is the hydraulic radius, s the channel gradient,
b
Subcritical flow Supercritical flow and n the Manning roughness coefficient, which is an
index of bed roughness and is usually estimated from
standard tables or by comparison with photographs of
channels of known roughness. Manning’s formula can
Stream bed
Stream bed be useful in estimating the discharge in flood conditions.
The height of the water can be determined from debris
stranded in trees and high on the bank. Only the channel
Figure 3.10 (a) Hydraulic jump. (b) Hydraulic drop. cross-section and the slope need measuring.

Fluvial erosion and transport
depth (Figure 3.10a). A hydraulic drop marks a change Streams are powerful geomorphic agents capable of
from subcritical to supercritical flow and is accompa- eroding, carrying, and depositing sediment. Stream
nied by a reduction in water depth (Figure 3.10b). These power is the capacity of a stream to do work. It may
abrupt changes in flow regimes may happen where there be expressed as:
is a sudden change in channel bed form, a situation
rife in mountain streams where there are usually large = ρgQs
obstructions such as boulders.
Flow velocity in streams is affected by the slope
gradient, bed roughness, and cross-sectional form of the where (omega) is stream power per unit length of
stream channel, ρ (rho) is water density, Q is stream
channel. It is very time-consuming to measure stream- discharge, and s is the channel slope. It defines the rate
flow velocity directly, and empirical equations have been at which potential energy, which is the product of the
devised to estimate mean flow velocities from read- weight of water, mg (mass, m, times gravitational accel-
ily measured channel properties. The Chézy equation, eration, g), and its height above a given datum, h,is
named after the eighteenth-century French hydraulic expended per unit length of channel. In other words,
engineer Antoine de Chézy, estimates velocity in terms stream power is the rate at which a stream works to
of the hydraulic radius and channel gradient, and a transport sediment, overcome frictional resistance, and
coefficient expressing the gravitational and frictional generate heat. It increases with increasing discharge and
forces acting upon the water. It defines mean flow increasing channel slope.
velocity, v, as:

√ Stream load
v = C Rs
All the material carried by a stream is its load. The
where R is the hydraulic radius, s is the channel gradient, total load consists of the dissolved load (solutes),
and C is the Chézy coefficient representing gravita- the suspended load (grains small enough to be sus-
tional and frictional forces. The Manning equation, pended in the water), and the bed load (grains too large